Create Grouped Stacked Bar Chart between Two Main Datasets and their Subdatasets

Question

I have two Datasets with their sub datasets (data per collection date); PROD's :PROD_0601, PROD_0615, PROD_0701

and then GAMMA's: GAMMA_GDv1, GAMMA_GDv2, GDv3

DS_GAMMA = {
  GAMMA_GDv1: {
      'cat1': 5,
      'cat2': 3,
       ...
      },
  GAMMA_GDv2: {
      'cat1': 5,
      'cat3': 7,
       ...
    },
   GAMMA_GDv3: {
      'cat1': 5,
      'cat2': 1,
       ...
    },
  }

DS_PROD = {
      PROD_0601: {
          'cat1': 5,
          'cat2':3,
           ...
          },
      PROD_0615: {
          'cat1': 5,
          'cat3': 7,
           ...
        },
       PROD_0701: {
          'cat1': 5,
          'cat2': 9,
           ...
        },
      }

I want to be able to to have a grouped stacked bar chart by each Cat showing the stacked PROD data and next to it GAMMA's stacked data per each Cat.

I have tried a few ways but I cannot get the data to be end-to-end stacked per each Cat as a column with the Gamma's same cat next to it stacked too.

I sketched on paper a small example for visual outcome.

Another Chart that looks like the outcome: